Finite Group Databasebeta

← #43248521

Subgroups — #43248521

Order 28352.

268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#28381932C211yesmaximal, characteristic, complemented
2#28381931C211yesmaximal, characteristic, complemented
3#28381914C211yesmaximal, characteristic, complemented
4#28381913C212yesmaximal, complemented
5#28381910C212yesmaximal, complemented
6#28381907C212yesmaximal, complemented
7#28381906C211yesmaximal, characteristic, complemented
8C2×#20296772C211yesmaximal, characteristic, complemented
9D8×D443C212yesmaximal, complemented
10#28381894C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C443C211yesmaximal, characteristic, complemented
12#20296788C2212yescomplemented
13#20296787—21no—
14#20296787C2211yescharacteristic
15#20296787C2211yescharacteristic, complemented
16#20296786—21no—
17#20296786C2212yescomplemented
18C2×D1772—21no—
19C2×D1772C2211yescharacteristic, complemented
20C2×C22⋊D443—22no—
21D4×D443—21no—
22D4×D443—22no—
23D4×D443C2212yescomplemented
24D4×D443C2212yescomplemented
25#20296777C2211yescharacteristic, complemented
26#20296776C2212yescomplemented
27#20296775C2211yescharacteristic, complemented
28#20296774C2211yescharacteristic, complemented
29D3544C2212yescomplemented
30#20296772C2211yescharacteristic, complemented
31#20296772C2212yescomplemented
32#20296772C2212yescomplemented
33#20296770C2212yescomplemented
34C2×C443⋊C8C2211yescharacteristic, complemented
35C8×D443C2212yescomplemented
36#41×C443C2211yescharacteristic, complemented
37C2×D4×C443C2211yescharacteristic, complemented
38SD16×C443C2212yescomplemented
39D8×C443C2212yescomplemented
40M16×C443C2211yescharacteristic, complemented
41C22×D443—21no—
42C22×D443—22no—
43C22×D443—22no—
44Dic886D411yescharacteristic
45Dic886C2311yescharacteristic
46D1772—22no—
47D1772—21no—
48D1772D411yescharacteristic
49D1772C2312yes—
50D1772C2311yescharacteristic
51C22⋊D443—21no—
52C22⋊D443—22no—
53C22⋊D443—22no—
54C22⋊D443—22no—
55C22⋊D443D412yes—
56C2×Dic443—22no—
57C4×D443—21no—
58C4×D443—22no—
59C4×D443C2312yes—
60C443⋊C8C2311yescharacteristic
61C443⋊C8C2311yescharacteristic
62C23×C443—21no—
63Q8×C443C2311yescharacteristic
64D4×C443—21no—
65D4×C443—21no—
66D4×C443C2311yescharacteristic
67D4×C443C2312yes—
68C2×C4×C443—21no—
69C2×C4×C443C2311yescharacteristic
70C8×C443C2312yes—
71C22×C443—21no—
72C22×C443—22no—
73C22×C443—81no—
74C22×C443C2×D411yescharacteristic
75C2×D443—21no—
76C2×D443—22no—
77C2×D443—82no—
78C2×D443—82no—
79C2×D443—81no—
80C2×D443C2×D412yes—
81C4×C443—21no—
82C4×C443C2×D411yescharacteristic
83C4×C443C2411yescharacteristic
84Dic443—21no—
85Dic443C2×D412yes—
86C2×C443—21no—
87C2×C443—41no—
88C2×C443—42no—
89C2×C443C22×D411yescharacteristic
90D443—22no—
91D443—41no—
92D443—42no—
93C443#57611yescharacteristic, complemented, Sylow
94#576—4431nomaximal, Sylow
95H(5,𝔽2)—4431no—
96H(5,𝔽2)—4431no—
97AGL(1,ℤ/8)—4432no—
98AGL(1,ℤ/8)—4432no—
99AGL(1,ℤ/8)—4431no—
100AGL(1,ℤ/8)D44311yescharacteristic, complemented
101#135—4431no—
102#135—4432no—
103C2×D8—4431no—
104C2×D8—4432no—
105#131—4431no—
106#41—8861no—
107#41—8861no—
108#41—4432no—
109#41—4432no—
110#41—4431no—
111#41—4431no—
112#41C2×D44311yescharacteristic, complemented
113C2×D4—8861no—
114C2×D4—8862no—
115C2×D4—8861no—
116C2×D4—8862no—
117C2×D4—4432no—
118C2×D4—4432no—
119C2×D4—4431no—
120C2×D4C2×D44311yescharacteristic, complemented
121Q16—4431no—
122SD16—4431no—
123SD16—4431no—
124SD16—4432no—
125SD16C2×D44312yescomplemented
126D8—4432no—
127D8—4431no—
128D8—4432no—
129D8—4432no—
130D8C2×D44312yescomplemented
131M16—4432no—
132M16C2×D44311yescharacteristic, complemented
133C2×C8—4431no—
134C2×C8—4432no—
135C23—21no—
136C23—8862no—
137C23—8862no—
138C23—8861no—
139Q8—4431no—
140Q8—4431no—
141Q8C22×D44311yescharacteristic
142D4—21no—
143D4—21no—
144D4—8862no—
145D4—8862no—
146D4—8861no—
147D4—8862no—
148D4—8862no—
149D4—8861no—
150D4—4432no—
151D4—4431no—
152D4—4432no—
153D4—4431no—
154D4C22×D44312yes—
155D4C22×D44311yescharacteristic
156C2×C4—21no—
157C2×C4—8862no—
158C2×C4—8862no—
159C2×C4—8861no—
160C2×C4—4432no—
161C2×C4C22×D44311yescharacteristic
162C8—4431no—
163C8—4431no—
164C8C22×D44312yes—
165C22—21no—
166C22—22no—
167C22—81no—
168C22—8862no—
169C22—8861no—
170C22—4432no—
171C22—35441no—
172C22—35442no—
173C22—35442no—
174C22D4×D44311yescharacteristic
175C4—21no—
176C4—8861no—
177C4—4432no—
178C4D4×D44311yescharacteristic
179C4C23×D44311yescharacteristic
180C2—21no—
181C2—42no—
182C2—41no—
183C2—8862no—
184C2—17722no—
185C2—17721no—
186C2C2×D4×D44311yescharacteristic
subgroupG/H
centerC2C2×D4×D443
commutator, cosocleC4×C443C24
FrattiniC4C23×D443
FittingAGL(1,ℤ/8)×C443C2
socleC2×C443C22×D4
hypercenterAGL(1,ℤ/8)D443
hypocenterC443#576
LCSG ▷ C4×C443 ▷ C2×C443 ▷ C443
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #28381932C2semidirect
2. #28381931C2semidirect
3. #28381914C2semidirect
4. #28381913C2semidirect
5. #28381910C2semidirect
6. #28381907C2semidirect
7. #28381906C2semidirect
8. C2×#20296772C2semidirect
9. D8×D443C2semidirect
10. #28381894C2semidirect
11. AGL(1,ℤ/8)×C443C2semidirect
12. #20296788C22semidirect
15. #20296787C22semidirect
17. #20296786C22semidirect
19. C2×D1772C22semidirect
23. D4×D443C22semidirect
24. D4×D443C22semidirect
25. #20296777C22semidirect
26. #20296776C22semidirect
27. #20296775C22semidirect
28. #20296774C22semidirect
29. D3544C22semidirect
30. #20296772C22semidirect
31. #20296772C22semidirect
32. #20296772C22semidirect
33. #20296770C22semidirect
34. C2×C443⋊C8C22semidirect
35. C8×D443C22semidirect
36. #41×C443C22semidirect
37. C2×D4×C443C22semidirect
38. SD16×C443C22semidirect
39. D8×C443C22semidirect
40. M16×C443C22semidirect
93. C443#576semidirect
100. AGL(1,ℤ/8)D443semidirect
112. #41C2×D443semidirect
120. C2×D4C2×D443semidirect
125. SD16C2×D443semidirect
130. D8C2×D443semidirect
132. M16C2×D443semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#283819322
#283819312
#283819142
#283819132
#283819102
#283819072
#283819062
C2×#202967722
D8×D4432
#283818942
AGL(1,ℤ/8)×C4432
#576443